Question

A ray of light from a lamp is inclined at an angle of 30 to the normal. If the image of the lamp formed is 10cm from the mirror
Determine the Distance between the lamp and it's image

Answer 1

To determine the distance between the lamp and its image, we will use the concept of reflection.

From the given information, we know that the angle of incidence (angle between the incident ray and the normal) is 30 degrees.

Since the light ray is reflecting off a mirror, the angle of reflection will be equal to the angle of incidence.

In this case, the angle of reflection is also 30 degrees.

We can draw a diagram to visualize the situation:

L N I
| / /
| / /
| / /
|/ /
*-----I'

In the diagram, the lamp is represented by "L". "N" represents the normal to the mirror surface, and "I" represents the incident ray.

The image of the lamp is formed at point "I'" which is 10cm away from the mirror.

We need to find the distance between the lamp "L" and its image "I'".

We can use trigonometry to find this distance.

The distance between the lamp "L" and the mirror surface is the hypotenuse of a right-angled triangle.

Using the angle of incidence, we can determine the length of the adjacent side of the triangle.

In this case, the adjacent side is equal to the distance between the mirror and the image, which is 10cm.

We can use the cosine function to find the length of the hypotenuse:

cos(30 degrees) = adjacent/hypotenuse
cos(30 degrees) = 10cm/hypotenuse

We can rearrange this equation to solve for the hypotenuse:

hypotenuse = 10cm / cos(30 degrees)

Using a calculator, we can find the value of cos(30 degrees) is approximately 0.866.

Therefore, the distance between the lamp and its image is approximately:

hypotenuse = 10cm / 0.866 ≈ 11.55cm

So, the distance between the lamp and its image is approximately 11.55cm.